Could anyone give an insight on how to prove the following formula? 

$$\sum_{n=-\infty}^{+\infty}J_{n}(\alpha)J_{N+n}(\alpha)=\delta_{N0} \, ,$$

where $N$ is an integer. I checked many references but failed to figure out the calculation method. By the way, I found this relation during some numerical calculations about Bessel functions.

Thank you very much in advance.